Digital sampling rate conversion of color TV signal

ABSTRACT

A converter to translate a sampled color television video signal, consisting of four pulse-code-modulated 8-bit digital samples during each cycle of the color subcarrier, to a corresponding signal consisting of three pulse-code-modulated 8-bit digital samples during each cycle of the color subcarrier. The four 8-bit samples from present and preceeding cycles are stored in several 8-bit input registers. The 8-bit sample in one of the input registers is coupled to an output register once per cycle. Two predetermined weighted combinations of 8-bit samples in predetermined ones of the input registers are coupled to second and third output registers once per cycle.

This invention relates to converters for translating a sampled colortelevision video digital signal consisting of a given number of digitalsamples during each cycle of the color subcarrier, to a digital signalhaving a different number of digital samples during each cycle of thecolor subcarrier. A color television video signal in the usual analogform can be translated to a digital form by making four digital samplesper cycle of the subcarrier, or by making three digital samples percycle of the subcarrier. Since the color subcarrier frequency is 3.58MHz, the four samples per cycle occur at a rate of 14.32 MHz and providea very high quality digital signal. Three samples per cycle occur at alower rate of 10.74 MHz and provide a digital signal which can be moreeconomically transmitted over a narrower band channel. The presentinvention is useful, for example, to convert from four digital samplesper subcarrier cycle to three digital samples per subcarrier cycle. Thelatter signal is more suitable for economical transmission to and from asatellite in earth orbit. A known method of making the conversion is touse a digital-to-analog converter to convert the signal with foursamples per cycle to an analog video signal, and then use ananalog-to-digital converter to convert the analog signal to a digitalsignal with three samples per cycle. This known method introducesdistortion which somewhat degrades the quality of the television signal.

According to an example of the invention, a digital-to-digitalconversion is made from four samples per color subcarrier cycle to threesamples per subcarrier cycle by giving predetermined weights topredetermined digital samples occurring during present and precedingcycles, and by making predetermined combinations of the weighted samplesto form three output samples during each cycle of the color subcarrier.

In the drawing:

FIG. 1 is a block diagram of a system constructed according to theteachings of the invention;

FIG. 2 is a schematic detailed diagram of one portion of FIG. 1;

FIG. 3 is a timing diagram which will be referred to in describing theoperation of FIG. 1;

FIG. 4 is a table showing the nomenclature applied tosuccessively-received digital samples.

FIG. 5 is a block diagram of an alternative construction for the shiftregisters in FIG. 1;

FIG. 6 is a block diagram of an arithmetic unit useful in the system ofFIG. 1;

FIG. 7 is a chart of filter characteristics which will be referred to indescribing how weighting constants are derived; and

FIG. 8 is a chart of calculated variations in signal/distortion ratiowith frequency when described approximate coefficients are used.

In FIG. 1, four serial digital samples per color subcarrier cycle from asource 8 are coupled over an 8-conductor bus 9 to inputs of fourthree-stage 8-bit-parallel shift registers 10, 11, 12 and 13. Threestage shift register 10 operates at time t₀ to gate an 8-bit digitalsample in parallel from first-stage 8-bit register 20 to second-stage8-bit register 21, and to gate a later-received 8-bit sample from8-conductor bus 9 to first-stage 8-bit register 20. A third-stageregister 21 is not used. Three-stage shift register 11 operates in asimilar manner at time t₁ to gate a sample from first-stage register 22to second-stage register 23, and a later sample from bus 9 tofirst-stage register 22. A third-stage register 23 is not used.Likewise, three-stage shift register 12 operates at time t₂ to gate asample from second-stage register 25 to third-stage register 26, a latersample from first-stage register 24 to second-stage register 25, and astill later sample from bus 9 to first-stage register 24; andthree-stage shift register 13 operates at time t₃ to gate a sample fromsecond-stage register 28 to third-stage register 29, a later sample fromfirst-stage register 27 to second-stage register 28, and a still latersample from bus 9 to first-stage register 27. The three-stage shiftregister 13 is shown in detail in FIG. 2. Each of stages 27, 28 and 29includes a storage register for 8-bit samples.

At a time t₄ following time t₃, the four registers 20, 22, 24 and 27contain respective 8-bit digital samples received during a present cycleof the color subcarrier, the four registers, 21, 23, 25 and 28 containrespective 8-bit samples received during a cycle of the color subcarrierprevious to the present cycle, and registers 26 and 29 contain 8-bitsamples received during a next earlier cycle of the color subcarrier.

At this time t₄, a system of parallel gates 30 transfers the 8-bitsamples in each of seven registers 20, 21, 23, 25, 26, 28 and 29 to anarithmetic unit 32. The timing pulses t₀ through t₄ repeated during eachcycle of the subcarrier are shown in FIG. 3.

FIG. 4 shows the nomenclature used for successively-received digitalsamples. The first sample x₀ of the present cycle is called x₄ and iscontained in register 24 at time t₄. The four samples x₀, x₁, x₂ and x₃of the previously received cycle are contained in registers 21, 23, 25and 28, respectively, at time t₄. The two samples x₂ and x₃ of thenext-previously received cycle are called x₋₂ and x₋₁ and are containedin registers 26 and 29 respectively, at time t₄.

It will be noted that some of the registers 20 through 29 in the fourthree-stage shift registers 10 through 13 are not used in the specificexample illustrated in FIG. 1. A more economical implementationincluding simply seven storage registers and transfer gates for the four8-bit samples is shown in FIG. 5. The operation of FIG. 5 is clear whenone begins with acceptance of the first sample x₂ at time t₂ andproceeds through times t₃, t₀, t₁, t₂, t₃ and t₀.

The arithmetic unit 32 in FIG. 1 which will be described in connectionwith FIG. 6, produces three 8-bit digital signal samples which arepresent at time t₄ of each cycle of the color subcarrier in 8-bitregisters 40, 41 and 42, and these samples are successively gated out inserial fashion at times t₀, t₅ and t₆ of the next following cycle to an8-conductor output line 46, where they form a serial succession of 8-bitsamples each transmitted in parallel on eight conductors.

The arithmetic unit shown in detail in FIG. 6 includes a connection 50from input terminal x₀ to y₀, whereby the x₀ digital sample of thefour-samples-percycle output signal becomes the y₀ digital sample of thethree-sample-per-cycle output signal.

The y₁ output of the arithmetic unit is derived by combining weightedsamples of inputs x₄, x₃, x₂, x₁, x₀ and x₋₁. The 8-bit input digitalsample x₄ is divided by 2⁵ by shifting the signal five spaces to theright in a shift register unit 52 labeled SR5. Sample x₃ is divided by2⁴ in unit 54 labeled SR4, and is divided by 2⁵ in a unit 55 labeledSR5. The outputs of units 54 and 55 are added in an adder 56. Otherdigital samples are divided and added by adders 57, 58 and 59 in amanner obvious from the drawing. The outputs of unit 52, adders 56through 59 and unit 60 are combined in an adder 62, which produces anoutput sample y₁. In a similar manner, the units and adders 64 producean output sample y₂.

The particular numbers by which the four input samples are divided, andthe combinations in which the divided samples are added, and the sumscombined in the arithmetic unit of FIG. 6 are determined by a techniquefor determining the sample values at a sampling rate equal to threetimes the color subcarrier. The description of the technique is dividedinto three sections. In the first section the constructed sample will berepresented as a weighted sum of the original samples, the weightingsbeing determined by a filter. Several filters will be investigated, andthe one which uses the fewest of the original samples to construct thenew sample will be chosen. In the second section, thesignal-to-distortion ratio of the resulting signal will be determined.To determine this ratio, the spectrum of a typical TV signal will beused. The distortion will be weighted to reflect the expected severityof distortion in different segments of the frequency band. In the thirdsection, the weighting factors will be modified, so that the circuit canbe implemented using adders rather than dividers, and then perturbed toobtain a local maximum in the signal-to-distortion ratio. The resultingcircuit will use between one and six old sample values to construct anew sample. It will provide a 74 dB signal-to-weighted distortion ratioin a 4.5 MHz band.

I. choice of Weighting Functions

A signal X(t), sampled once every T seconds, results in a signal##EQU1## The frequency spectrum of the resulting signal contains theoriginal frequency spectrum plus displaced versions of that spectrum. Toreconstruct the original signal the sampled signal is filtered by g(t),which eliminates the displaced spectra. The resulting signal is:##EQU2## If this signal is sampled every 4/3 T seconds, ##EQU3## The newsamples are thus represented as a weighted sum of the previous samples.The conversion between sampling rates can be effected by multiplying theold samples by constants, determined by a filter, and summing. Due tothe symmetry of the problem, the same weighting functions will be usedto determine every third one of the constructed samples. Separatecircuits must be constructed to determine y(0), y (4/3 T), and y (8/3T), and this circuitry can be used to determine all other samples.

To realize this circuit, the summation in equation 1 must be truncatedto some finite value. This value depends on the filter chosen and theamount of distortion which can be tolerated. Initially, all weightingcoefficients less than 1/512 were ignored. The reason for choosing thislevel is that the sampled signal is quantized to 256 levels. If theweighting factor is less than 1/512, it cannot add more than 1/2 aquantization level to the constructed sample, and will most likely noteffect the final value.

Using this criterion, over 200 of the original samples are required toconstruct each new sample, if a rectangular low pass filter is used todetermine the weighting coefficients. This means the conversion circuitwould require over 600 multipliers and adders. To reduce the complexityof this circuit filters with more gradual skirts in the frequency domainwere considered. Among the filters considered were those withtriangular, raised-cosine and gaussian skirts.

The filters are flat in the frequency range 0→f₁, have a skirt in thefrequency range f₁ →f₂, and are zero above f₂. In general, the largerthe skirt the smaller the number of original samples required toconstruct a new sample. Assuming that the original signal had spectralcomponents from 0 to 6 MHz, and that we are interested in the spectrumbetween 0 and 4.5 MHz in the constructed signal, the following phenomenaare encountered as the skirt is increased:

If f₁ is less than 4.5 MHz the signal spectrum is distorted.

If f₂ is greater than 5.37 MHz, the spectrum of the original signalbetween 5.37 and 6 MHz is aliased into the range between 4.74 and 5.37MHz. This component does not affect the region of interest in the newsignal.

If f₂ is greater than 8.32 MHz, the displaced version of the originalspectrum is not completely eliminated and is aliased back into theconstructed signal spectrum.

Taking these phenomena into account, and assuming the signal energy inthe range between 4.2 and 6 MHz is small in comparison to the energybetween 0 and 4.2 MHz, skirts were designed to fill the band between 4.2and 10.12 MHz. A raised-cosine skirt in this range reduced the number ofsignificant weighting coefficients from over 200, for the low-passfilter, to 21. A filter with a gaussian skirt was investigated. Theresponse of this filter was down 50 dB at 10.74 MHz, where the shiftedversion of the color subcarrier occurs. This requirement made thisfilter look more like a low-pass filter than the raised cosine filter,and, increased the number of significant weighting coefficients.

It is possible to obtain faster convergence in the time domain usinggaussian filters, than it is using raised cosine filters. This benefitwas not realized in this instance because of the severity of theconstraint on attenuation at a high frequency. Various arrangements ofgaussian functions were investigated to try to obtain this potentialimprovement, and, it was found that the convergence could be made fasterby defining a split gaussian filter, as shown in FIG. 5, and as definedby the following equations: ##EQU4## The following constraints wereplaced on the design of this filter:

Both the function and its first derivative are continuous at F1.

The attenuation is down 53 dB at 3×3.58 MHz, where the displaced colorsubcarrier occurs.

The signal-to-distortion is 53 dB at 3.58 MHz. The constraints set k1 =EXP [η² /k2 - Ln2] and ##EQU5## Therefore, k1 and k2 are determined bypicking η. The constant η was adjusted to obtain the fewest significantweighting coefficients. This filter reduced the number of significantweighting coefficients from 21 to 9.

Ii. signal/Distortion

The filtering techniques introduce distortion into the signal spectrum,because of the phenomena described in Section I, and the seriestruncation performed. This distortion will be calculated.

The constructed signal is: ##EQU6## where F_(N) (X) is a function of theoriginal samples.

    ______________________________________                                         ##STR1##                                                                 

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It is noted that the relationship between y(k(4/3)T) and the originalsamples X(NT), is the same as the relationship between y(k+3j) (4/3)T)and the original samples X((N+4j)T). The constructed signal cantherefore be represented as: ##EQU7## where ##EQU8## That is, the F_(j)(X(t)) is the weighted sum of certain of the samples.

Every third one of the constructed samples lines up with one of theoriginal samples. It was found that when the filter has the type ofsymmetry, about 2·3.58 MHz displayed by the split gaussian and raisedcosine filters, the constructed sample equals the original sample itlines up with. Furthermore, it was noted that the coefficientmultiplying the sample at T-iT, when determining the sample at 4/3 T, isthe same as the coefficient multiplying the sample at 3T+iT, whendetermining the sample at 8/3 T. This is expected from the symmetry ofthe samples in the time domain. The constructed signal can therefore berepresented as: ##EQU9## where, ##EQU10## Taking the fourier transformof the constructed signal, and simplifying, one obtains, ##EQU11## wheref_(c) is 3.58 MHz, and X(f) is the spectrum of the original TV signal.

To construct the estimated signal from Y(f), it is passed through a lowpass filter with a cut-off at 4.5 MHz. The distortion component is:##EQU12##

To calculate the distortion it is necessary to assume a signal spectrum.The spectrum used in these calculations is taken from D. G. Fink,Television Engineering Handbook, McGraw-Hill Book Company, 1957, pg.10-22. According to Fink, the spectra of a set of 27 slides provided bythe Eastman Kodak Company for the National Television System Committee,has the following characteristics:

The luminance component decreases in amplitude at a rate ofapproximately 6 dB per octave in the range from 0.0157 to 0.75 MHz, 10dB per octave from 0.75 to 4 MHz, and 12 dB per octave above 4 MHz.

The chrominance components decrease at about 7 dB per octave in therange from 15.7 to 400 kHz, 5 dB per octave from 0.4 to 1.5 MHz on theside toward the picture carrier, and 9 dB per octave from 0.4 to 1.5 MHzon the side away from the picture carrier.

The ratio of the peak luminance amplitude to the peak chrominanceamplitude is about 5 to 1.

For a particular set of weighting coefficients, this calculationprovides a distortion spectrum for the band of the TV signal. It hasbeen suggested that distortion in all regions of the band are notequally objectionable. In particular, it is felt that distortion in thelow frequency region of the band and distortion in the region near thecolor subcarrier is much more objectionable than distortion near the 2MHz region, and distortion near the high end of the band. While aquantitative measure of objectionability for this type of distortion isnot available, several weighting functions for white noise have beenestablished. The CCIR noise weighting function: ##EQU13##

F₁ = 0.27 MHz,

F₂ = 1.37 MHz,

F₃ = 0.39 MHz,

emphasizes distortion in the regions in which it should be mostobjectionable. This function was uesd to weight the distortion powerspectrum.

Iii. modification of Multiplication Coefficients

The significant multiplicative coefficients, obtained from the splitgaussian filter, were:

A₋₄ = -0.00986

A₋₃ = 0.03516

A₋₂ = -0.10840

A₋₁ = 0.38672

A₀ = 0.81250

A₁ = 0.15820

A₂ = 0.05176

A₃ = 0.01465

A₄ = 0.00293.

To implement this circuit in hardware it is desirable to represent A_(i)as ##EQU14## where b_(i),j is zero or one. This representation enablesthe multiplication to be performed by adding displaced versions of theoriginal sample, rather than performing multiplication by a constantless than one. In addition, it may be possible to modify thesecoefficients to improve the signal to distortion ratio.

The following procedure was used to obtain a set of A_(i) which can berepresented in the desired manner, and provide a local optimum in thesignal-to-weighted distortion ratio. Letting L = 10, the coefficientsA_(i) were approximated by ##EQU15## The signal-to-weighted distortionratio was calculated for this set of approximate A_(i), and, for each ofthe eighteen sets of A_(i) in which one of these A_(i) were increased ordecreased by 2^(-L). The approximate set of A_(i) was replaced by theset of perturbed A_(i) which provided the largest signal-to-distortionratio. The new set of A_(i) were perturbed, and, the procedure wasrepeated until a local optimum was obtained. The approximate A_(i),resulting from this procedure, were approximated by a new set of A_(i)with L = 8. The perturbation procedure was repeated to obtain a newlocal optimum. Finally, the entire procedure was repeated for L = 6. Thefollowing set of A_(i) resulted from this procedure:

A₋₄ = 0

A₋₃ = 0.03125 = 2⁻⁵

A₋₂ = -0.09375 = -[⁻⁴ + 2⁻⁵ ]

A₋₁ = 0.375 = 2⁻² + 2⁻³

A₀ = 0.8125 = 2⁻¹ + 2⁻² + 2⁻⁴

A₁ = -0.15625 = - [2⁻³ + 2⁻⁵ ]

A₂ = 0.03125 = 2⁻⁵

A₃ = 0

A₄ = 0

The peak-to-peak signal power-to-mean square weighted noise power wascalculated as follows. The mean square signal power was calculated bynumerically integrating the square of the amplitude signal spectrum,between 0 and 4.5 MHz. Assuming the signal levels to be uniformlydistributed between +V and -V, S_(p).p was calculated to be 12·S_(m)·s.The amplitude spectrum of the noise was calculated by the procedurespecified in section II. The square of this spectrum was weighted by theCCIR noise weighting factor and numerically integrated. The resultingsignal-to-distortion ratio for the approximate set of A_(i) is 73.9 dB.

The procedure was repeated for small intervals in the band of thesignal. The signal-to-weighted distortion ratio at different frequenciesin the band is plotted in FIG. 8.

Using the results of the foregoing calculations, seven digital samplesx₋₂, x₋₁, x₀, x₁, x₂, x₃ and x₄ as shown in FIGS. 1 and 4 are weightedand combined in the manner illustrated in the arithmetic unit shown inFIG. 6. The converter system of FIG. 1 operates in a manner which hasbeen described and with the timing shown in FIG. 3 to translate a videosource of four serial digital 8-bit samples per cycle of the colorsubcarrier signal on 8-bit bus 9 to three serial digital 8-bit samplesper cycle of the color subcarrier signal on 8-bit output bus 46.

What is claimed is:
 1. A converter to translate a color television videosignal consisting of four digital samples during each cycle of the colorsubcarrier to a corresponding signal consisting of three digital samplesduring each cycle of the color subcarrier, comprisinga plurality ofinput registers connected to receive a respective plurality ofsuccessive digital samples, three output registers for three outputdigital samples per cycle of the color subcarrier, means to couple thecontents of one of said input registers to one of said three outputregisters, means to weight and combine the contents of predeterminedones of said input registers and couple the result to a second one ofsaid three output registers, means to weight and combine the contents ofpredetermined ones of said input register and couple the result to athird one of said three output registers, and means to couple thecontents of said three output registers in sequence at the cycle rate toan output channel.
 2. A converter according to claim 1 wherein saiddigital samples each consist of plurality of pulse code modulated bits,and each of said input registers and output registers consists of anequal plurality of parallel stages.
 3. A converter according to claim 2wherein said input registers comprise four multi-bit shift registerseach receiving and shifting in parallel the plurality of bits of arespective one of the four digital samples at the cycle rate, wherebystages of the shift register contain digital samples from a presentcycle and at least one preceding cycle.
 4. A converter according toclaim 1 which each of said means to weight and combine the contents ofpredetermined ones of said input registers comprises arithmetic shiftregisters in which a digital sample is shifted to the right to dividethe digital number by the number of shifts.
 5. A converter according toclaim 4 wherein each of said means to weight and combine the contents ofpredetermined ones of said input registers also comprises adder meansfor combining the outputs of said arithmetic shift registers.